Application of Discontinuous Galerkin spectral method on hexahedral elements for aeroacoustic

Nicolas Castel 1 Gary Cohen 1 Marc Durufle 1, 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : A discontinuous Galerkin method is developed for linear hyperbolic systems on general hexahedral meshes. The use of hexahedral elements and tensorized quadrature formulas to evaluate the integrals leads to an efficient matrix-vector product. It is shown for high order approximations, the reduction in computational time can be very important, compared to tetrahedral elements. Two choices of quadrature points are considered, the Gauss points or Gauss-Lobatto points. The method is applied to the aeroacoustic system (simplified Linearized Euler Equations). Some 3-D numericals experiments show the importance of penalization, and the advantage of using high order.
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Nicolas Castel, Gary Cohen, Marc Durufle. Application of Discontinuous Galerkin spectral method on hexahedral elements for aeroacoustic. Journal of Computational Acoustics, World Scientific Publishing, 2009, 17 (2), pp.175-196. ⟨hal-00403787⟩

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